Research uncovers improved zero-free regions for dedekind zeta-functions, indicating advancements for low-lying zeros in number fields.
Given a number field L≠ Q, we obtain new and explicit zero-free regions for Dedekind zeta-functions of L, which refine the previous works of Ahn--Kwon, Kadiri, and Lee. In particular, for low-lying zeros, we extend Kadiri's result to all number fields while improving the main constant.
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Das et al. (2025) studied this question.